This paper addresses the problem of target detection against a background of clutter by using frequency snapshots with reduced degrees of freedom (DOF). We derive the optimal detector under the Neyman-Pearson criterion for general frequency snapshots selection with arbitrary DOF. If the clutter statistics are known/well-estimated, a greedy method for selecting the frequency snapshots is presented. For unknown clutter statistics, we employ a uniform random frequency snapshot selection method and show how the DOF employed affects the detection performance.